The sum of two angles is $87^\circ$. Angle 2 is $163^\circ$ smaller than $4$ times angle 1. What are the measures of the two angles in degrees?
Explanation: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 87}$ ${y = 4x-163}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${4x-163}$ for $y$ in the first equation. ${x + }{(4x-163)}{= 87}$ Simplify and solve for $x$ $ x+4x - 163 = 87 $ $ 5x-163 = 87 $ $ 5x = 250 $ $ x = \dfrac{250}{5} $ ${x = 50}$ Now that you know ${x = 50}$ , plug it back into $ {y = 4x-163}$ to find $y$ ${y = 4}{(50)}{ - 163}$ $y = 200 - 163$ ${y = 37}$ You can also plug ${x = 50}$ into $ {x+y = 87}$ and get the same answer for $y$ ${(50)}{ + y = 87}$ ${y = 37}$ The measure of angle 1 is $50^\circ$ and the measure of angle 2 is $37^\circ$.